Abstract
Modelling the evolution of complex life history traits and behavioural patterns observed in the natural world is a challenging task. Here, we develop a novel computational method to obtain evolutionarily optimal life history traits/behavioural patterns in population models with a strong inheritance. The new method is based on the reconstruction of evolutionary fitness using underlying equations for population dynamics and it can be applied to self-reproducing systems (including complicated age-structured models), where fitness does not depend on initial conditions, however, it can be extended to some frequency-dependent cases. The technique provides us with a tool to efficiently explore both scalar-valued and function-valued traits with any required accuracy. Moreover, the method can be implemented even in the case where we ignore the underlying model equations and only have population dynamics time series. As a meaningful ecological case study, we explore optimal strategies of diel vertical migration (DVM) of herbivorous zooplankton in the vertical water column which is a widespread phenomenon in both oceans and lakes, generally considered to be the largest synchronised movement of biomass on Earth. We reveal optimal trajectories of daily vertical motion of zooplankton grazers in the water column depending on the presence of food and predators. Unlike previous studies, we explore both scenarios of DVM with static and dynamic predators. We find that the optimal pattern of DVM drastically changes in the presence of dynamic predation. Namely, with an increase in the amount of food available for zooplankton grazers, the amplitude of DVM progressively increases, whereas for static predators DVM would abruptly cease.
Highlights
Complex behavioural responses and sophisticated life history traits of individual organisms observed in the natural world should have a great influence on ecological processes, and we often need to incorporate them in our population and ecosystem models to be able to improve their forecasting power
We introduce a new method of computation of the evolutionarily optimal life history traits and behavioural patterns which is based on the approximation of the fitness function(al)
This idea is close to the wellknown generic concept of fitness in evolutionary biology: it is often assumed that natural selection should result in an increase of the organism’s fitness; the evolutionarily optimal behaviour would correspond to a maximum of the fitness function subject to some trade-offs (Wright 1932; Roff 1992; Davies et al 2012; Birch 2016)
Summary
Complex behavioural responses and sophisticated life history traits of individual organisms observed in the natural world should have a great influence on ecological processes (reproduction, competition, mortality, etc.), and we often need to incorporate them in our population and ecosystem models to be able to improve their forecasting power. We suggest a new computational method of finding the evolutionarily optimal strategy/life history trait which is based on an approximation of evolutionary fitness derived from the underlying model equations of population dynamics. We show that including a dynamic predator of zooplankton (e.g. the own predator biomass depends on the amount of zooplankton consumed) would produce different predictions of DVM as compared to the situation with static predators when the amount food (phytoplankton) available for zooplankton grazers in surface layers progressively increases This confirms the importance of considering dynamical feedback from the environment in evolutionary modelling and highlights limitations of the conventional approach of modelling DVM of zooplankton via maximisation of the reproductive value (Fiksen and Carlotti 1998; Sainmont et al 2015).
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